## University of Sydney Algebra Seminar

# Stephen Griffeth (Universidad de Talca, Chile)

## Monday 2nd December, 2:05-2:55pm, Carslaw 707A

### Monodromy representations of partial braid groups and finite dimensional rational Cherednik algebra modules (joint work with Armin Gusenbauer, Daniel Juteau, and Martina Lanini)

Each complex reflection group gives rise to a rational Cherednik algebra, whose representation theory is closely related to that of the Hecke algebra of the group. Bezrukavnikov and Etingof introduced functors of parabolic induction and restriction for rational Cherednik algebras, and observed that their functors inherit an action of certain fundamental groups. In this talk we focus instead on these monodromy representations, and explain how they may be used to produce practical necessary conditions for finite dimensionality of irreducible lowest weight modules.